KReF Offers Training-Free Time-Series Forecasting

Traditional probabilistic long-term time-series forecasting (LTSF) typically relies on complex trained models, while training-free conformal methods often provide only intervals around a point forecast. This paper introduces KReF, a novel training-free retrieval framework that addresses these limitations by treating retrieved historical futures as a query-local empirical predictive distribution. KReF operates by robustly preprocessing time-series data, embedding each lookback using handcrafted statistics or frozen random Fourier features, and then retrieving similar historical lookback-future pairs. The similarity weights derived from these pairs directly define predictive masses, quantiles, CRPS (Continuous Ranked Probability Score), and a weighted-mean point forecast. The framework further refines interval boundaries using a probability-integral-transform map and validation-selected expansion/shrinkage rates. Across six LTSF benchmarks and four horizons, KReF consistently achieved the lowest CRPS and often the lowest IS90, even matching or surpassing trained baselines for point forecasts on some datasets, all without any gradient-based fitting. An archive-oracle analysis suggests significant potential for further improvement.